Geometry of Higher Dimensional Algebraic Varieties: 26 (Oberwolfach Seminars, 26) - Softcover

Peternell, Thomas; Miyaoka, Joichi

Softcover

ISBN 10: 3764354909 ISBN 13: 9783764354909

Publisher: Birkhäuser, 1997

Synopsis

This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub­ ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex­ plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin­ stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

About this title

Review

"Contains nice historical notes and exercises... Many examples are given to illustrate the theory... Beautifully written [with] up-to-date references to the subjects... Highly recommended."

--ZAA

Synopsis

This is a book about the classification theory and geometry of higher dimensional varieties: existence and geometry of rational curves via characteristic p-methods, manifolds with negative Kodaira dimension, vanishing theorums, theory of extremal rays (Mori theory), and minimal models. It gives an introduction to this difficult and not readily accessible subject, and focuses on the spread of ideas rather than a deliberate inclusion of all proofs. The methods presented vary from complex analysis to complex algebraic geometry and algebraic geometry over fields of positive characteristics. It should be suitable for students in algebraic geometry and complex analysis as well as researchers in these fields and experts from other fields who require an overview of the theory.

Edition details

• Publisher: Birkhäuser
• Publication date: 1997
• Language: English
• ISBN 10: 3764354909
• ISBN 13: 9783764354909
• Binding: Paperback
• Number of pages: 224